What are the different approaches used in Machine Learning?
Things in italics should give you enough googleable terms to start a deeper dive :P.
There are 3 main branches of statistical ML.

Supervised Learning
This approach is taken when a problem can be phrased as associating some $X$ with some $Y$. For example, classifying a picture of a cat ($X$) with the label “Cat” ($Y$). Training in supervised learning usually means presenting some $X$, having an agent predict the label, comparing the prediction with the answer to get an error metric, and finally using the error to update the agent to make better predictions on future $X$s. MNIST is a great example of a classification domain.
1.1 Supervised learning also works with regression when we want to learn an associated number instead of a label, such as the risk of heart disease given years of smoking and weight.

Unsupervised Learning
This type of learning is used when we want to draw inferences from a dataset without labeled responses. It can be used to find hidden patterns or grouping in data.

Reinforcement Learning
The $X$s and $Y$s in supervised learning are i.i.d., meaning that they don’t relate to the previous $X$ that a model has previously observed. However, there are many problems where the most recent $X$, $X$ at time $t$ ($X_t$), is very important to figuring out what $Y$ to predict ($Y_{t+1}$) for the next $X$ ($X_{t+1}$). The field of reinforcement learning (RL) builds on this notion by framing observations as data that is generated by an agent interacting with an environment. Specifically, the field of RL poses the problem of finding a behaviour (a policy) to select actions such that an agent using the policy can maximize a special signal called the reward from the environment. The agent starts in a state of the world ($S_t$) at time $t$ and takes some action ($A_t$) which puts it in a new state ($S_{t+1}$) and gives it a reward ($R_{t+1}$).


Neural networks are a technique for finding features (some kinda notable differences) in data. They can be used in all of the above learning strategies but are not necessary for them although their application has had some very powerful results recently. Deep ___ learning is simply the application of a multilayered neural network on one of the above learning methods.